The equation of common tangent to the circle $x^{2} + y^{2} = 2 a^{2}$ and the parabola $y^{2} = 8 a x$ is

y = - x - 2 a

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

y - x + 2 a = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

y = x + 2 a

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

y + x = 2 a

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct options are
A $y = - x - 2 a$
B $y = x + 2 a$
Equation of tangent to $y^{2} = 8 a x$ is $y = m x + \frac{2 a}{m}$
To be the tangent to the circle, perpendicular distance from centre must equal radius
$m y - m^{2} x - 2 a = 0$
$\frac{2 a}{\sqrt{m^{2} + m^{4}}} = \sqrt{2} a$
$m = 1, - 1$
Option A,C

Suggest Corrections

Similar questions

x^{2} + y^{2} = 2 a^{2}

y^{2} = 8 a x

y = \pm (x + 2 a)

x^{2} + y^{2} = 2 a^{2}

y^{2} = 8 a x

Equation of the common tangent to the parabola $y^{2} = 24 x$ and the circle $x^{2} + y^{2} = 18$ is

x^{2} = - 8 a y

x^{2} + y^{2} = a^{2}

a^{2}

Join BYJU'S Learning Program